Question

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Answer 1

1. x = 4

2. x = 20

Explanation:

1.

ΔABC and ΔAJK are similar (AA). Therefore the sides are in proportion:

`(AC)/(AJ)=(AB)/(AK)`

We have:

AC = 1 + 4 = 5

AJ = 1

AB = 1 + x

AK = 1

Substitute:

`(5)/(1)=(1+x)/(1)`

`5=1+x` subtract 1 from both sides

`4=x\to x=4`

2.

ΔVUT and ΔVMN are similar (AA). Therefore the sides are in proportion:

`(VU)/(VM)=(VT)/(VN)`

We hve:

VU = x + 8

VM = x

VT = 49

VN = 49 - 14 = 35

Substitute:

`(x+8)/(x)=(49)/(35)` cross multiply

`35(x+8)=49x` use the distributive property a(c + b) = ab + ac

`35x+280=49x` subtract 35x from both sides

`280=14x` divide both sides by 14

`20=x\to x=20`